There is considerable interest across several industries in developing metrology systems for precisely and accurately measuring physical properties of surfaces, and thin films deposited on surfaces. Optical techniques are often preferable because they can be performed during a manufacturing process without contacting a test article. Typically, an apparatus measures light before and after interacting with a test surface. Surface properties may then be inferred according to a theory of the interaction and an understanding of the operating principles of the apparatus.
To be useful, a metrology system must be precise as well as accurate. Precision refers to a capability to make fine measurements. Accuracy, in contrast, refers a difference between a value obtained from measurement and a true value of the physical property being measured. Generally, a highly precise system is not necessarily highly accurate.
Obtaining high accuracy typically requires understanding system characteristics both theoretically and through calibration. In many applications, however, detailed characterization of the entire measurement system is difficult, or impractical, or simply unwarranted by the desired accuracy of the measurement. Thus, high precision measurements are often not as accurate as they could be because a user interprets a measured signal with a technique that simplifies the operating principles of the measuring apparatus.
Two trends in the semiconductor industry point to a need for improved calibration techniques. First, there is an ever-present trend toward higher measurement accuracy arising from demands for thinner films and more stringent process standards. For example, the currently recommended upper bound on uncertainty in reflectivity measurements is 0.1%.
Second, there is an important trend toward integrating process and metrology tools by locating metrology tools closer to manufacturing process lines. Presently, most metrology systems “stand alone,” physically removed from the process tools. Away from the process line, space is not at an economic premium. Accordingly, most “stand-alone” metrology systems opt for immovable optical heads and motion stages that move a test article under the optics. Fixed to a massive frame, the optical systems of stand-alone devices are stable over long periods of time. In contrast, integrating metrology and process tools drives designs having movable optics because space is at a premium near the process line and movable optics significantly reduce the size of a metrology device's “footprint.” As compared to fixing the optical head and moving the test article, however, moving the optical head over the test surface requires closer attention to the manner and frequency of calibration because of the movements.
Two examples of common approaches to calibration illustrate the technical problem addressed by this invention. One simple calibration method regards that a signal S relates to a physical quantity of interest Q by:S=αQ  (Eqn. 1)In Eqn. 1, α contains information from the measurement system and Q is the physical quantity of interest. With this simple relationship between the signal and the quantity of interest, one can remove the information relating to the measurement system and arrive at a relative determination of Q by taking the ratio of two independent measurements
                                          S            2                                S            1                          =                              Q            2                                Q            1                                              (                  Eqn          .                                          ⁢          2                )            Comparing the two equations, above, the factor α dropped out in Eqn. 2. Thus, if a relative determination of the desired quantity suffices for the purposes of the measurement, it is not necessary to know the characteristics of the measurement system embodied in the factor α, including any position-dependencies.
U.S. Pat. No. 5,747,813 exemplifies the approach, above, by teaching a method for determining a relative reflectance of a wafer with dual beam reflectometer. See col. 2, lines 31–41. In U.S. Pat. No. 5,747,813, knowledge about the reflectometer characteristics, such as optical efficiencies, detector gains and noise is not necessary to arrive at a relative reflectivity of the wafer. Such information “drops out” because of the ratio, above. Relative reflectivity is useful, for example, in monitoring process consistency on a wafer-to-wafer basis. For an absolute determination, U.S. Pat. No. 5,747,813 teaches further use of ratios to reference to a known standard. See col. 2, lines 31–41.
Relative measurements are simple, convenient and adequate for some uses. Often, however, a measurement system behaves in a more complicated manner than Eqn. 1 suggests. For example, one may interpret a signal S as relating to a physical quantity of interest Q by:S=αQ+β  (Eqn. 3)
In Eqn. 3, α and β both relate to the measurement system. Comparing Eqn. 3 to Eqn. 1, just one additional factor, β, disallows simply forming a ratio from two experiments to remove the information about the measurement system. The factors relating to the measurement system simply do not drop out from a ratio.
In curve fitting, one presupposes a mathematical form of a family of curves and determines coefficients that fit data points “best.” Common mathematical forms include polynomials, often with many terms. FIG. 1 illustrates the curve fitting approach. FIG. 1 includes data points 100, and curves 110–130. The data points represent signal values at a corresponding value of the physical quantity of interest. The different curves are for different possible mathematical forms that “fit” the data.
FIG. 1 shows that many different orders of polynomials “fit” the data, even when there is no position dependence. This is a drawback in that a range of curves that fit the data is an uncertainty that may limit the accuracy of a measurement. If the range of curves is substantial compared to the desired accuracy of the measurement (0.1% or less in the semiconductor industry), a more rigorous interpretation of the data is useful, if not essential. Moreover, with moving optics, the calibration problem is significantly complicated because of position-dependencies.
Therefore, because of new demands for movable optical systems with position-dependent characteristics and a continuing broad demand for greater accuracy, there is a need for calibration techniques and associated components that enable detailed, position-dependent characterization of a metrology system.